Add tensor scan op

This is the initial implementation a generic scan operation.
Based on this, cumsum and cumprod method have been added to TensorBase.

unsupported/Eigen/CXX11/src/Tensor/TensorScan.h

@@ -0,0 +1,197 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Igor Babuschkin <igor@babuschk.in>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_SCAN_H
+#define EIGEN_CXX11_TENSOR_TENSOR_SCAN_H
+namespace Eigen {
+
+namespace internal {
+template <typename Op, typename XprType>
+struct traits<TensorScanOp<Op, XprType> >
+    : public traits<XprType> {
+  typedef typename XprType::Scalar Scalar;
+  typedef traits<XprType> XprTraits;
+  typedef typename XprTraits::StorageKind StorageKind;
+  typedef typename XprType::Nested Nested;
+  typedef typename remove_reference<Nested>::type _Nested;
+  static const int NumDimensions = XprTraits::NumDimensions;
+  static const int Layout = XprTraits::Layout;
+};
+
+template<typename Op, typename XprType>
+struct eval<TensorScanOp<Op, XprType>, Eigen::Dense>
+{
+  typedef const TensorScanOp<Op, XprType>& type;
+};
+
+template<typename Op, typename XprType>
+struct nested<TensorScanOp<Op, XprType>, 1,
+            typename eval<TensorScanOp<Op, XprType> >::type>
+{
+  typedef TensorScanOp<Op, XprType> type;
+};
+} // end namespace internal
+
+/** \class TensorScan
+  * \ingroup CXX11_Tensor_Module
+  *
+  * \brief Tensor scan class.
+  *
+  */
+
+template <typename Op, typename XprType>
+class TensorScanOp
+    : public TensorBase<TensorScanOp<Op, XprType>, ReadOnlyAccessors> {
+public:
+  typedef typename Eigen::internal::traits<TensorScanOp>::Scalar Scalar;
+  typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
+  typedef typename XprType::CoeffReturnType CoeffReturnType;
+  typedef typename Eigen::internal::nested<TensorScanOp>::type Nested;
+  typedef typename Eigen::internal::traits<TensorScanOp>::StorageKind StorageKind;
+  typedef typename Eigen::internal::traits<TensorScanOp>::Index Index;
+
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorScanOp(
+      const XprType& expr, const Index& axis, const Op& op = Op())
+      : m_expr(expr), m_axis(axis), m_accumulator(op) {}
+
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  const Index axis() const { return m_axis; }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  const XprType& expression() const { return m_expr; }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+  const Op accumulator() const { return m_accumulator; }
+
+protected:
+  typename XprType::Nested m_expr;
+  const Index m_axis;
+  const Op m_accumulator;
+};
+
+// Eval as rvalue
+template <typename Op, typename ArgType, typename Device>
+struct TensorEvaluator<const TensorScanOp<Op, ArgType>, Device> {
+
+  typedef TensorScanOp<Op, ArgType> XprType;
+  typedef typename XprType::Index Index;
+  static const int NumDims = internal::array_size<typename TensorEvaluator<ArgType, Device>::Dimensions>::value;
+  typedef DSizes<Index, NumDims> Dimensions;
+  typedef typename XprType::Scalar Scalar;
+  typedef typename XprType::CoeffReturnType CoeffReturnType;
+  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
+
+  enum {
+    IsAligned = false,
+    PacketAccess = (internal::packet_traits<Scalar>::size > 1),
+    BlockAccess = false,
+    Layout = TensorEvaluator<ArgType, Device>::Layout,
+    CoordAccess = false,
+    RawAccess = true
+  };
+
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorEvaluator(const XprType& op,
+                                                        const Device& device)
+      : m_impl(op.expression(), device),
+        m_device(device),
+        m_axis(op.axis()),
+        m_accumulator(op.accumulator()),
+        m_dimensions(m_impl.dimensions()),
+        m_size(m_dimensions[m_axis]),
+        m_stride(1),
+        m_output(NULL) {
+
+    // Accumulating a scalar isn't supported.
+    EIGEN_STATIC_ASSERT(NumDims > 0, YOU_MADE_A_PROGRAMMING_MISTAKE);
+    eigen_assert(m_axis >= 0 && m_axis < NumDims);
+
+    // Compute stride of scan axis
+    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+      for (int i = 0; i < m_axis; ++i) {
+        m_stride = m_stride * m_dimensions[i];
+      }
+    } else {
+      for (int i = NumDims - 1; i > m_axis; --i) {
+        m_stride = m_stride * m_dimensions[i];
+      }
+    }
+  }
+
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const {
+      return m_dimensions;
+  }
+
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(Scalar* data) {
+    m_impl.evalSubExprsIfNeeded(NULL);
+    if (data) {
+      accumulateTo(data);
+      return false;
+    } else {
+      m_output = static_cast<CoeffReturnType*>(m_device.allocate(dimensions().TotalSize() * sizeof(Scalar)));
+      accumulateTo(m_output);
+      return true;
+    }
+  }
+  
+  template<int LoadMode>
+  EIGEN_DEVICE_FUNC PacketReturnType packet(Index index) const {
+    return internal::ploadt<PacketReturnType, LoadMode>(m_output + index);
+  }
+
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType* data() const
+  {
+    return m_output;
+  }
+
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const
+  {
+    return m_output[index];
+  }
+
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void cleanup() {
+    if (m_output != NULL) {
+      m_device.deallocate(m_output);
+      m_output = NULL;
+    }
+    m_impl.cleanup();
+  }
+
+protected:
+  TensorEvaluator<ArgType, Device> m_impl;
+  const Device& m_device;
+  const Index m_axis;
+  Op m_accumulator;
+  const Dimensions& m_dimensions;
+  const Index& m_size;
+  Index m_stride;
+  CoeffReturnType* m_output;
+
+  // TODO(ibab) Parallelize this single-threaded implementation if desired
+  EIGEN_DEVICE_FUNC void accumulateTo(Scalar* data) {
+    // We fix the index along the scan axis to 0 and perform an
+    // scan per remaining entry. The iteration is split into two nested
+    // loops to avoid an integer division by keeping track of each idx1 and idx2.
+    for (Index idx1 = 0; idx1 < dimensions().TotalSize() / m_size; idx1 += m_stride) {
+       for (Index idx2 = 0; idx2 < m_stride; idx2++) {
+          // Calculate the starting offset for the scan
+          Index offset = idx1 * m_size + idx2;
+
+          // Compute the prefix sum along the axis, starting at the calculated offset
+          CoeffReturnType accum = m_accumulator.initialize();
+          for (Index idx3 = 0; idx3 < m_size; idx3++) {
+            Index curr = offset + idx3 * m_stride;
+            m_accumulator.reduce(m_impl.coeff(curr), &accum);
+            data[curr] = m_accumulator.finalize(accum);
+          }
+       }
+    }
+  }
+};
+
+}  // end namespace Eigen
+
+#endif  // EIGEN_CXX11_TENSOR_TENSOR_SCAN_H